The main theme of this paper is the connection between the existence of infinitely many periodic orbits for a Hamiltonian system and the behavior of its action or index spectrum under iterations. We use the action and index spectra to show that any Hamiltonian diffeomorphism of a closed, rational manifold with zero first Chern class has infinitely many periodic orbits and that, for a general ra...

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom, a saddle point (called the Stark saddle point) appears. For energies slightly above the saddle point energy, one can find classical orbits that are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths, observing structural chan...

This paper focuses on symmetric potentials subjected to periodic driving. Four unperturbed potentials V0(r) were considered, namely the Plummer potential and Dehnen potentials with γ = 0.0, 0.5, and 1.0, each subjected to a time-dependence of the form V (r, t) = V0(r)(1 +m0 sinωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particula...

We study the conditions that favour boxiness of isodensities in the face-on views of orbital 3D models for barred galaxies. Using orbital weighted profiles we show that boxiness is in general a composite effect that appears when one considers stable orbits belonging to several families of periodic orbits. 3D orbits that are introduced due to vertical instabilities play a crucial role in the fac...

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn [5] where a numerical technique is also proposed. Our algorithms consist of s...

Resonant orbits have been widely employed in mission design for planetary flyby trajectories (JEO) and, more recently, as a source of long-term stability (IBEX). Yet, resonant orbits have not been explored extensively as transfer mechanisms between non-resonant orbits in multi-body systems. To highlight the benefit of employing resonant orbits for transfers and given the increased interest in e...

We show that, for a certain class of systems, the problem of establishing the existence of periodic orbits can be successfully studied by means of a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate positions of periodic points, and the existence of periodic orbits in a neighborhood of these approximations is proved using an interval operat...

This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number ...

We study the dynamics near transverse intersections of stable and unstable manifolds of sheets of symmetric periodic orbits in reversible systems. We prove that the dynamics near such homoclinic and heteroclinic intersections is not C1 structurally stable. This is in marked contrast to the dynamics near transverse intersections in both general and conservative systems, which can be C1 structura...

Orbits of known extrasolar planets that are located outside the tidal circular-ization regions of their parent stars are often substantially eccentric. By contrast, planetary orbits in our Solar System are approximately circular, reflecting planet formation within a nearly axisymmetric, circumsolar disk. We propose that the remarkable elongations of extrasolar planetary orbits are a consequence...